Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 587, 460, 511 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 587, 460, 511 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 587, 460, 511 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 587, 460, 511 is 1.
HCF(587, 460, 511) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 587, 460, 511 is 1.
Step 1: Since 587 > 460, we apply the division lemma to 587 and 460, to get
587 = 460 x 1 + 127
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 127 and 460, to get
460 = 127 x 3 + 79
Step 3: We consider the new divisor 127 and the new remainder 79, and apply the division lemma to get
127 = 79 x 1 + 48
We consider the new divisor 79 and the new remainder 48,and apply the division lemma to get
79 = 48 x 1 + 31
We consider the new divisor 48 and the new remainder 31,and apply the division lemma to get
48 = 31 x 1 + 17
We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get
31 = 17 x 1 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 587 and 460 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(48,31) = HCF(79,48) = HCF(127,79) = HCF(460,127) = HCF(587,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 511 > 1, we apply the division lemma to 511 and 1, to get
511 = 1 x 511 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 511 is 1
Notice that 1 = HCF(511,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 587, 460, 511?
Answer: HCF of 587, 460, 511 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 587, 460, 511 using Euclid's Algorithm?
Answer: For arbitrary numbers 587, 460, 511 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.